2026-07-20T05:28:40Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6301 2024-03-06T10:37:40Z ddc:004 open_access

Popular Half-Integral Matchings Kavitha, Telikepalli bipartite graphs stable matchings fractional matchings polytopes In an instance G = (A union B, E) of the stable marriage problem with strict and possibly incomplete preference lists, a matching M is popular if there is no matching M0 where the vertices that prefer M' to M outnumber those that prefer M to M'. All stable matchings are popular and there is a simple linear time algorithm to compute a maximum-size popular matching. More generally, what we seek is a min-cost popular matching where we assume there is a cost function c : E -> Q. However there is no polynomial time algorithm currently known for solving this problem. Here we consider the following generalization of a popular matching called a popular half-integral matching: this is a fractional matching ~x = (M_1 + M_2)/2, where M1 and M2 are the 0-1 edge incidence vectors of matchings in G, such that ~x satisfies popularity constraints. We show that every popular half-integral matching is equivalent to a stable matching in a larger graph G^*. This allows us to solve the min-cost popular half-integral matching problem in polynomial time. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Telikepalli Kavitha 2016 Is Part Of LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2016.22 urn:nbn:de:0030-drops-63011 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.22 eng https://creativecommons.org/licenses/by/3.0/legalcode